An apparatus of the type defined in the opening paragraph is known, for example from DE 27 47 383 A1. The known apparatus is a shaving apparatus for cutting facial hairs. The first cutter of said shaving apparatus is formed by an arcuately mounted shear foil and the second cutter is formed by a lamellar cutter comprising steel blades embedded in an arched plastics part. The drive member is formed by a drive pin having a partly spherical head at its free end. This head engages an undercut cylindrical recess in the plastics part of the lamellar cutter. The head and the recess form a joint for the transmission of the driving force from the drive pin to the lamellar cutter. In order to ensure that the head transmits the driving force within the closest possible range of the point of application of the resultants of the frictional forces between the shear foil and the lamellar cutter, the driving pin should be comparatively long and its head should project deep into the interior of the arched plastics part of the lamellar cutter in order to act on this plastics part as near as possible to the blades which cooperate with the shear foil. These requirements impose an undesirable restriction on the construction and in many cases can be met only with great difficulty or not at all. With such a construction it is, for example, not possible to drive the reciprocatingly drivable toothed cutter of a toothed cutting device having two associated flat toothed cutters in such a manner that the driving force is transmitted in the area of the point of application of the resultants of the frictional forces between the two toothed cutters because this point of application is situated in the area of the two associated contact surfaces of the two flat toothed cutters and a spherical head of a drive pin cannot extend into this area of the contact surfaces.